caa a22 4500 445363142 CHVBK 20180317142921.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s00780-010-0137-5 doi (NATIONALLICENCE)springer-10.1007/s00780-010-0137-5 Unbiased and efficient Greeks of financial options [Elektronische Daten] [Yuh-Dauh Lyuu, Huei-Wen Teng] The price of a derivative security equals the discounted expected payoff of the security under a suitable measure, and Greeks are price sensitivities with respect to parameters of interest. When closed-form formulas do not exist, Monte Carlo simulation has proved very useful for computing the prices and Greeks of derivative securities. Although finite difference with resimulation is the standard method for estimating Greeks, it is in general biased and suffers from erratic behavior when the payoff function is discontinuous. Direct methods, such as the pathwise method and the likelihood ratio method, are proposed to differentiate the price formulas directly and hence produce unbiased Greeks (Broadie and Glasserman, Manag. Sci. 42:269-285, 1996). The pathwise method differentiates the payoff function, whereas the likelihood ratio method differentiates the densities. When both methods apply, the pathwise method generally enjoys lower variances, but it requires the payoff function to be Lipschitz-continuous. Similarly to the pathwise method, our method differentiates the payoff function but lifts the Lipschitz-continuity requirements on the payoff function. We build a new but simple mathematical formulation so that formulas of Greeks for a broad class of derivative securities can be derived systematically. We then present an importance sampling method to estimate the Greeks. These formulas are the first in the literature. Numerical experiments show that our method gives unbiased Greeks for several popular multi-asset options (also called rainbow options) and a path-dependent option. Springer-Verlag, 2010 Option pricing nationallicence Rainbow options nationallicence Path-dependent options nationallicence Monte Carlo simulation nationallicence Greeks nationallicence Importance sampling nationallicence Lyuu Yuh-Dauh Dep artment of Finance and Department of Computer Science and Information Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, 106, Taipei, Taiwan aut Teng Huei-Wen Graduate Institute of Statistics, National Central University, Jhongda Rd., No. 300, 32049, Jhongli City, Taoyuan County, Taiwan aut Finance and Stochastics Springer-Verlag 15/1(2011-01-01), 141-181 0949-2984 15:1<141 2011 15 780 https://doi.org/10.1007/s00780-010-0137-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00780-010-0137-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lyuu Yuh-Dauh Dep artment of Finance and Department of Computer Science and Information Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, 106, Taipei, Taiwan aut NATIONALLICENCE 700 1- Teng Huei-Wen Graduate Institute of Statistics, National Central University, Jhongda Rd., No. 300, 32049, Jhongli City, Taoyuan County, Taiwan aut NATIONALLICENCE 773 0- Finance and Stochastics Springer-Verlag 15/1(2011-01-01), 141-181 0949-2984 15:1<141 2011 15 780 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer